The technical field of the examples to be disclosed in the following sections is generally related to the art of image projection, and more particularly, to method of projecting images using individually addressable pixels having curved reflective surfaces.
Projection systems using spatial light modulators having individually addressable pixels each of which has a reflective surface, such as micromirrors, produce images by modulating light beams with the pixels. Resolution of the produced images is determined by the total number of addressable pixels involved in producing the image. However, the number of addressable pixels in a single spatial light modulator is subject to many limitations in both manufacturing and device design.
An advanced approach for obtaining high perceived resolution of the produced images, for example, using a spatial light modulator with a lower resolution to accomplish produced images with a higher perceived resolution, is by projecting images of the pixel array of the spatial light modulator onto different locations on the screen. Viewer's eyes integrate the interlaced pixel images of the array, and perceive a high resolution. This approach, however, has many disadvantages, which is demonstrated in FIG. 1A to FIG. 1F.
For demonstration purpose, assuming image 10 with 4×4 resolution is to be produced as shown in FIG. 1A. Each square represents an image pixel with solid and shaded squares presenting “white” and “black” pixels. This image can be produced using a spatial light modulator with lower resolution, such as 2×2 pixel array 12. The corresponding images (P1, P2, P3, and P4) of the 2×2 pixel array is shown in FIG. 1B. The images of the 2×2 pixel array are circulated to different locations as shown in FIG. 1C to FIG. 1E. Specifically, at time t=t0, the image of the 2×2 pixel array is located at the upper left corner and frame 0 is loaded to display the first pattern. At time t=t0+T/2 with T being the moving period, the image of the 2×2 pixel array is moved to the bottom left corner; and frame 1 is loaded to display the second pattern. At time t=t0+T/4 the image of the 2×2 pixel array is moved to the bottom right corner; and frame 2 is loaded to display the third pattern. At time t=t0+3T/4 the image of the 2×2 pixel array is moved to the upper right corner; and frame 3 is loaded to display the third pattern. If the entire moving cycle is fast enough, for example faster than the flicker time of human eyes, viewer's eyes integrate the four interlaced patterns without perceiving the moving. The viewer perceives the produced image having a resolution of 4×4.
This approach has disadvantages, one of which is low “fill factor” of the pixels in the spatial light modulator. Fill factor is referred to as the ratio between the total area of the pixels of the pixel array in the spatial light modulator and the total area of the pixel array. In the example as shown in FIG. 1F, the fill factor of the pixel array is calculated as the reflective area of the nine pixels to area 13 of the nine pixel array.
When the above technique is employed to achieve a higher perceived image resolution using a pixel array with a lower resolution (the total number of individually addressable pixels in the array), the area of the individual pixel has to be reduced in order to avoid superposition of the image pixels at different locations. Avoiding such image pixel superposition is critical to contrast ratio of the produced images. Reduction of the individual pixel area, however, increases the gaps between the pixels. The increased gap, in turn, reduces the fill factor, and degrades the system contrast ratio by exposing more non-reflective areas (e.g. areas introducing light scattering) to the incident illumination light. For the array of micromirrors, such as DMD, as an example, the fill factor can be reduced to 25%, as schematically illustrated in FIG. 1F. This problem can be exasperated when the illumination light incident onto the pixels and to be modulated exhibits angular expansion (which is often the case), as schematically illustrated in FIGS. 2A and 2B.
Referring to FIG. 2A, collimated incident light beams 14 are reflected by flat (non-curved) reflective surface 18 of a pixel that is an addressable micromirror. The reflected light beams extend spatially as it propagates. The overall profile of the reflected light beam in a plane parallel to and above the mirror plate is extended, as shown in FIG. 2B, wherein the cross-section of each reflected beam intersected by the plane is illustrated with dash-line circles. As a result, the image of the mirror plate generated from the over all profile of the reflected light beams is larger than the physical size of the mirror plate. Because the overall profile is larger than the physical size of the mirror plate, the illumination intensity of the image pixel corresponds to the mirror plate may be reduced, as well as the contrast ratio.